Wittgenstein on Mathematics by Severin Schroeder

Author:Severin Schroeder [Schroeder, Severin]
Language: deu
Format: epub
Tags: Philosophie
Publisher: Taylor and Francis
Published: 2020-12-29T23:00:00+00:00

but he is right to conclude that such people, presented by Wittgenstein to illustrate the possibility of using radically different concepts, may ‘not be fully intelligible to us’

(298). For our concepts reflect our concerns and interests and our ways of thinking.

Conventionalism 123

not to volume), but clearly that doesn’t make their calculations incorrect.

And that is the way, I take it, Wittgenstein wants us to regard cases of

strangely different forms of mathematics, too: not as erroneous, not as

false claims about reality, but as tools that are used in an odd and prob-

ably impractical way. In the wood merchants’ case, the tools are like

ours, but applied in an odd way which strikes us as stupid; in the earlier

example of distributing nuts, the tool itself appeared unsuitable (unless

strange things happened). But in neither case are the tools, the calcula-

tions as such, to be assessed as false.

If a mathematical equation were a statement of fact, it could be true

or false independently of people’s beliefs. We could then imagine a whole

community to believe erroneously that 2 × 2 = 5. But can we really?

But what would this mean: “Even though everybody believed that

2 × 2 were 5, it would still be 4”?—For what would it be like for

everybody to believe that?—Well, I could imagine, for instance, that

people had a different calculus, or a technique which we wouldn’t

call “calculating”. But would it be wrong? (Is a coronation wrong?

To beings different from ourselves it might look extremely odd.)

( PPF §348; LW I §934)

The crucial point is that in order to attribute to a community a consid-

ered mathematical belief that 2 × 2 = 5 we’d have to imagine them as

having a corresponding mathematical practice: a calculus and its applica-

tions. What they believe in mathematics is a reflection of what they do in calculating and applying mathematics. Hence if we can indeed imagine

them having such a practice, the corresponding belief would be true as a

matter of course. So our criticism cannot be that their belief is untrue (it

isn’t if it correctly reflects their practice), it can only be that their practice is utterly impractical or even ludicrous (cf. RFM I §§152–3: 95). Moreover, we should probably not regard it as ‘calculating’ or a form of what

we like to call ‘mathematics’.

The same applies to the case of traders that do not insist that the price

be proportional to the quantity of the goods sold. We can imagine such a

practice, although we find it rather incomprehensible, if not insane. But

here, as in the 2 × 2 = 5 example above, Wittgenstein reminds us of familiar elements in our own culture that to rational outsiders may appear

bizarre, such as the ceremony of a coronation ( RFM I §153: 95). And

as he notes that we may find ‘ 2 × 2 = 5’ too odd to be called ‘mathematics’, just as we may refuse to call a deviant transition from one sentence

to another (e.g. from ‘ p ˅ q’ to ‘ p’) ‘logical’ or ‘inferring’ ( RFM I §116: 80)—similarly, Wittgenstein would obviously agree

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